Dr Frosh removed the original retweet, but then posted it again, adding: "I don't agree any mainstream party is like Nazis."

She said: "I've explained... on Twitter that I retweeted someone who was highlighting a quote from Hitler showing he (Hitler) believed he was a socialist.

"They [Nazis] are so far removed from mainstream political thought that they should be thought of as completely apart and not an extreme version of any mainstream party. The terms far-left or far-right are misleading.

"I have also made it clear that I did not agree with the tweet and do not consider Labour and/or socialists associated in any way with them and I would not want people to think that."

Dr Frosh has added a disclaimer to her Twitter account, reading: "Tweets are in a personal capacity and retweets are by no means an endorsement."

Mr Lloyd said: "I will not be rushing to judgement but I am obviously concerned. I will be seeing Rachel to discuss the matter over the next couple of days.

"It is not something that I would have done. The commissioner and deputy commissioner are public and high-profile roles. We must recognise that everything we do is open for scrutiny."

Dr Frosh said: "David is, of course, right. I have already said I shouldn't have retweeted it."